/********************************************************************
*                                                                  *
* THIS FILE IS PART OF THE OggSQUISH SOFTWARE CODEC SOURCE CODE.   *
*                                                                  *
********************************************************************



> From xiphmont@MIT.EDU Tue Jun  3 14:50:15 1997
> Subject: Re: fft.c
> Date: Tue, 03 Jun 1997 14:50:11 EDT
> From: Monty <xiphmont@MIT.EDU>
>
> The include files are not really necessary; they define a few macros
> depending on the compiler in use (eg, STIN becomes one of "static" or
> "static inline") and the prototypes for the functions in fft.c.  You
> should be able to compile and use the code without the headers with
> minimal modification.  The C code behaves nearly identically to the
> fortran code; inspection of the code should clarify the differences
> (eg, the 'ifac' argument).  Let me know if you need any other help
> with the code.
>
> Monty




file: fft.c
function: Fast discrete Fourier and cosine transforms and inverses
author: Monty <xiphmont@mit.edu>
modifications by: Monty
last modification date: Jul 1 1996

********************************************************************/

/* These Fourier routines were originally based on the Fourier
routines of the same names from the NETLIB bihar and fftpack
fortran libraries developed by Paul N. Swarztrauber at the National
Center for Atmospheric Research in Boulder, CO USA.  They have been
reimplemented in C and optimized in a few ways for OggSquish. */

/* As the original fortran libraries are public domain, the C Fourier
routines in this file are hereby released to the public domain as
well.  The C routines here produce output exactly equivalent to the
original fortran routines.  Of particular interest are the facts
that (like the original fortran), these routines can work on
arbitrary length vectors that need not be powers of two in
length. */

#include <math.h>
#include "ogg.h"
#include "fft.h"

static void drfti1(int n, float *wa, int *ifac){
	static int ntryh[4] = { 4, 2, 3, 5 };
	static float tpi = 6.28318530717958647692528676655900577;
	float arg, argh, argld, fi;
	int ntry = 0, i, j = -1;
	int k1, l1, l2, ib;
	int ld, ii, ip, is, nq, nr;
	int ido, ipm, nfm1;
	int nl = n;
	int nf = 0;

L101:
	j++;
	if (j < 4)
		ntry = ntryh[j];
	else
		ntry += 2;

L104:
	nq = nl / ntry;
	nr = nl - ntry*nq;
	if (nr != 0) goto L101;

	nf++;
	ifac[nf + 1] = ntry;
	nl = nq;
	if (ntry != 2)goto L107;
	if (nf == 1)goto L107;

	for (i = 1; i<nf; i++){
		ib = nf - i + 1;
		ifac[ib + 1] = ifac[ib];
	}
	ifac[2] = 2;

L107:
	if (nl != 1)goto L104;
	ifac[0] = n;
	ifac[1] = nf;
	argh = tpi / n;
	is = 0;
	nfm1 = nf - 1;
	l1 = 1;

	if (nfm1 == 0)return;

	for (k1 = 0; k1<nfm1; k1++){
		ip = ifac[k1 + 2];
		ld = 0;
		l2 = l1*ip;
		ido = n / l2;
		ipm = ip - 1;

		for (j = 0; j<ipm; j++){
			ld += l1;
			i = is;
			argld = (float)ld*argh;
			fi = 0.;
			for (ii = 2; ii<ido; ii += 2){
				fi += 1.;
				arg = fi*argld;
				wa[i++] = cos(arg);
				wa[i++] = sin(arg);
			}
			is += ido;
		}
		l1 = l2;
	}
}

void __ogg_fdrffti(int n, float *wsave, int *ifac){

	if (n == 1) return;
	drfti1(n, wsave + n, ifac);
}

void __ogg_fdcosqi(int n, float *wsave, int *ifac){
	static float pih = 1.57079632679489661923132169163975;
	static int k;
	static float fk, dt;

	dt = pih / n;
	fk = 0.;
	for (k = 0; k<n; k++){
		fk += 1.;
		wsave[k] = cos(fk*dt);
	}

	__ogg_fdrffti(n, wsave + n, ifac);
}

STIN void dradf2(int ido, int l1, float *cc, float *ch, float *wa1){
	int i, k;
	float ti2, tr2;
	int t0, t1, t2, t3, t4, t5, t6;

	t1 = 0;
	t0 = (t2 = l1*ido);
	t3 = ido << 1;
	for (k = 0; k<l1; k++){
		ch[t1 << 1] = cc[t1] + cc[t2];
		ch[(t1 << 1) + t3 - 1] = cc[t1] - cc[t2];
		t1 += ido;
		t2 += ido;
	}

	if (ido<2)return;
	if (ido == 2)goto L105;

	t1 = 0;
	t2 = t0;
	for (k = 0; k<l1; k++){
		t3 = t2;
		t4 = (t1 << 1) + (ido << 1);
		t5 = t1;
		t6 = t1 + t1;
		for (i = 2; i<ido; i += 2){
			t3 += 2;
			t4 -= 2;
			t5 += 2;
			t6 += 2;
			tr2 = wa1[i - 2] * cc[t3 - 1] + wa1[i - 1] * cc[t3];
			ti2 = wa1[i - 2] * cc[t3] - wa1[i - 1] * cc[t3 - 1];
			ch[t6] = cc[t5] + ti2;
			ch[t4] = ti2 - cc[t5];
			ch[t6 - 1] = cc[t5 - 1] + tr2;
			ch[t4 - 1] = cc[t5 - 1] - tr2;
		}
		t1 += ido;
		t2 += ido;
	}

	if (ido % 2 == 1)return;

L105:
	t3 = (t2 = (t1 = ido) - 1);
	t2 += t0;
	for (k = 0; k<l1; k++){
		ch[t1] = -cc[t2];
		ch[t1 - 1] = cc[t3];
		t1 += ido << 1;
		t2 += ido;
		t3 += ido;
	}
}

STIN void dradf4(int ido, int l1, float *cc, float *ch, float *wa1,
	float *wa2, float *wa3){
	static float hsqt2 = .70710678118654752440084436210485;
	int i, k, t0, t1, t2, t3, t4, t5, t6;
	float ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
	t0 = l1*ido;

	t1 = t0;
	t4 = t1 << 1;
	t2 = t1 + (t1 << 1);
	t3 = 0;

	for (k = 0; k<l1; k++){
		tr1 = cc[t1] + cc[t2];
		tr2 = cc[t3] + cc[t4];
		ch[t5 = t3 << 2] = tr1 + tr2;
		ch[(ido << 2) + t5 - 1] = tr2 - tr1;
		ch[(t5 += (ido << 1)) - 1] = cc[t3] - cc[t4];
		ch[t5] = cc[t2] - cc[t1];

		t1 += ido;
		t2 += ido;
		t3 += ido;
		t4 += ido;
	}

	if (ido<2)return;
	if (ido == 2)goto L105;

	t1 = 0;
	for (k = 0; k<l1; k++){
		t2 = t1;
		t4 = t1 << 2;
		t5 = (t6 = ido << 1) + t4;
		for (i = 2; i<ido; i += 2){
			t3 = (t2 += 2);
			t4 += 2;
			t5 -= 2;

			t3 += t0;
			cr2 = wa1[i - 2] * cc[t3 - 1] + wa1[i - 1] * cc[t3];
			ci2 = wa1[i - 2] * cc[t3] - wa1[i - 1] * cc[t3 - 1];
			t3 += t0;
			cr3 = wa2[i - 2] * cc[t3 - 1] + wa2[i - 1] * cc[t3];
			ci3 = wa2[i - 2] * cc[t3] - wa2[i - 1] * cc[t3 - 1];
			t3 += t0;
			cr4 = wa3[i - 2] * cc[t3 - 1] + wa3[i - 1] * cc[t3];
			ci4 = wa3[i - 2] * cc[t3] - wa3[i - 1] * cc[t3 - 1];

			tr1 = cr2 + cr4;
			tr4 = cr4 - cr2;
			ti1 = ci2 + ci4;
			ti4 = ci2 - ci4;
			ti2 = cc[t2] + ci3;
			ti3 = cc[t2] - ci3;
			tr2 = cc[t2 - 1] + cr3;
			tr3 = cc[t2 - 1] - cr3;


			ch[t4 - 1] = tr1 + tr2;
			ch[t4] = ti1 + ti2;

			ch[t5 - 1] = tr3 - ti4;
			ch[t5] = tr4 - ti3;

			ch[t4 + t6 - 1] = ti4 + tr3;
			ch[t4 + t6] = tr4 + ti3;

			ch[t5 + t6 - 1] = tr2 - tr1;
			ch[t5 + t6] = ti1 - ti2;
		}
		t1 += ido;
	}
	if (ido % 2 == 1)return;

L105:

	t2 = (t1 = t0 + ido - 1) + (t0 << 1);
	t3 = ido << 2;
	t4 = ido;
	t5 = ido << 1;
	t6 = ido;

	for (k = 0; k<l1; k++){
		ti1 = -hsqt2*(cc[t1] + cc[t2]);
		tr1 = hsqt2*(cc[t1] - cc[t2]);
		ch[t4 - 1] = tr1 + cc[t6 - 1];
		ch[t4 + t5 - 1] = cc[t6 - 1] - tr1;
		ch[t4] = ti1 - cc[t1 + t0];
		ch[t4 + t5] = ti1 + cc[t1 + t0];
		t1 += ido;
		t2 += ido;
		t4 += t3;
		t6 += ido;
	}
}

STIN void dradfg(int ido, int ip, int l1, int idl1, float *cc, float *c1,
	float *c2, float *ch, float *ch2, float *wa){

	static float tpi = 6.28318530717958647692528676655900577;
	int idij, ipph, i, j, k, l, ic, ik, is;
	int t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
	float dc2, ai1, ai2, ar1, ar2, ds2;
	int nbd;
	float dcp, arg, dsp, ar1h, ar2h;
	int idp2, ipp2;

	arg = tpi / (float)ip;
	dcp = cos(arg);
	dsp = sin(arg);
	ipph = (ip + 1) >> 1;
	ipp2 = ip;
	idp2 = ido;
	nbd = (ido - 1) >> 1;
	t0 = l1*ido;
	t10 = ip*ido;

	if (ido == 1)goto L119;
	for (ik = 0; ik<idl1; ik++)ch2[ik] = c2[ik];

	t1 = 0;
	for (j = 1; j<ip; j++){
		t1 += t0;
		t2 = t1;
		for (k = 0; k<l1; k++){
			ch[t2] = c1[t2];
			t2 += ido;
		}
	}

	is = -ido;
	t1 = 0;
	if (nbd>l1){
		for (j = 1; j<ip; j++){
			t1 += t0;
			is += ido;
			t2 = -ido + t1;
			for (k = 0; k<l1; k++){
				idij = is - 1;
				t2 += ido;
				t3 = t2;
				for (i = 2; i<ido; i += 2){
					idij += 2;
					t3 += 2;
					ch[t3 - 1] = wa[idij - 1] * c1[t3 - 1] + wa[idij] * c1[t3];
					ch[t3] = wa[idij - 1] * c1[t3] - wa[idij] * c1[t3 - 1];
				}
			}
		}
	}
	else{

		for (j = 1; j<ip; j++){
			is += ido;
			idij = is - 1;
			t1 += t0;
			t2 = t1;
			for (i = 2; i<ido; i += 2){
				idij += 2;
				t2 += 2;
				t3 = t2;
				for (k = 0; k<l1; k++){
					ch[t3 - 1] = wa[idij - 1] * c1[t3 - 1] + wa[idij] * c1[t3];
					ch[t3] = wa[idij - 1] * c1[t3] - wa[idij] * c1[t3 - 1];
					t3 += ido;
				}
			}
		}
	}

	t1 = 0;
	t2 = ipp2*t0;
	if (nbd<l1){
		for (j = 1; j<ipph; j++){
			t1 += t0;
			t2 -= t0;
			t3 = t1;
			t4 = t2;
			for (i = 2; i<ido; i += 2){
				t3 += 2;
				t4 += 2;
				t5 = t3 - ido;
				t6 = t4 - ido;
				for (k = 0; k<l1; k++){
					t5 += ido;
					t6 += ido;
					c1[t5 - 1] = ch[t5 - 1] + ch[t6 - 1];
					c1[t6 - 1] = ch[t5] - ch[t6];
					c1[t5] = ch[t5] + ch[t6];
					c1[t6] = ch[t6 - 1] - ch[t5 - 1];
				}
			}
		}
	}
	else{
		for (j = 1; j<ipph; j++){
			t1 += t0;
			t2 -= t0;
			t3 = t1;
			t4 = t2;
			for (k = 0; k<l1; k++){
				t5 = t3;
				t6 = t4;
				for (i = 2; i<ido; i += 2){
					t5 += 2;
					t6 += 2;
					c1[t5 - 1] = ch[t5 - 1] + ch[t6 - 1];
					c1[t6 - 1] = ch[t5] - ch[t6];
					c1[t5] = ch[t5] + ch[t6];
					c1[t6] = ch[t6 - 1] - ch[t5 - 1];
				}
				t3 += ido;
				t4 += ido;
			}
		}
	}

L119:
	for (ik = 0; ik<idl1; ik++)c2[ik] = ch2[ik];

	t1 = 0;
	t2 = ipp2*idl1;
	for (j = 1; j<ipph; j++){
		t1 += t0;
		t2 -= t0;
		t3 = t1 - ido;
		t4 = t2 - ido;
		for (k = 0; k<l1; k++){
			t3 += ido;
			t4 += ido;
			c1[t3] = ch[t3] + ch[t4];
			c1[t4] = ch[t4] - ch[t3];
		}
	}

	ar1 = 1.;
	ai1 = 0.;
	t1 = 0;
	t2 = ipp2*idl1;
	t3 = (ip - 1)*idl1;
	for (l = 1; l<ipph; l++){
		t1 += idl1;
		t2 -= idl1;
		ar1h = dcp*ar1 - dsp*ai1;
		ai1 = dcp*ai1 + dsp*ar1;
		ar1 = ar1h;
		t4 = t1;
		t5 = t2;
		t6 = t3;
		t7 = idl1;

		for (ik = 0; ik<idl1; ik++){
			ch2[t4++] = c2[ik] + ar1*c2[t7++];
			ch2[t5++] = ai1*c2[t6++];
		}

		dc2 = ar1;
		ds2 = ai1;
		ar2 = ar1;
		ai2 = ai1;

		t4 = idl1;
		t5 = (ipp2 - 1)*idl1;
		for (j = 2; j<ipph; j++){
			t4 += idl1;
			t5 -= idl1;

			ar2h = dc2*ar2 - ds2*ai2;
			ai2 = dc2*ai2 + ds2*ar2;
			ar2 = ar2h;

			t6 = t1;
			t7 = t2;
			t8 = t4;
			t9 = t5;
			for (ik = 0; ik<idl1; ik++){
				ch2[t6++] += ar2*c2[t8++];
				ch2[t7++] += ai2*c2[t9++];
			}
		}
	}

	t1 = 0;
	for (j = 1; j<ipph; j++){
		t1 += idl1;
		t2 = t1;
		for (ik = 0; ik<idl1; ik++)ch2[ik] += c2[t2++];
	}

	if (ido<l1)goto L132;

	t1 = 0;
	t2 = 0;
	for (k = 0; k<l1; k++){
		t3 = t1;
		t4 = t2;
		for (i = 0; i<ido; i++)cc[t4++] = ch[t3++];
		t1 += ido;
		t2 += t10;
	}

	goto L135;

L132:
	for (i = 0; i<ido; i++){
		t1 = i;
		t2 = i;
		for (k = 0; k<l1; k++){
			cc[t2] = ch[t1];
			t1 += ido;
			t2 += t10;
		}
	}

L135:
	t1 = 0;
	t2 = ido << 1;
	t3 = 0;
	t4 = ipp2*t0;
	for (j = 1; j<ipph; j++){

		t1 += t2;
		t3 += t0;
		t4 -= t0;

		t5 = t1;
		t6 = t3;
		t7 = t4;

		for (k = 0; k<l1; k++){
			cc[t5 - 1] = ch[t6];
			cc[t5] = ch[t7];
			t5 += t10;
			t6 += ido;
			t7 += ido;
		}
	}

	if (ido == 1)return;
	if (nbd<l1)goto L141;

	t1 = -ido;
	t3 = 0;
	t4 = 0;
	t5 = ipp2*t0;
	for (j = 1; j<ipph; j++){
		t1 += t2;
		t3 += t2;
		t4 += t0;
		t5 -= t0;
		t6 = t1;
		t7 = t3;
		t8 = t4;
		t9 = t5;
		for (k = 0; k<l1; k++){
			for (i = 2; i<ido; i += 2){
				ic = idp2 - i;
				cc[i + t7 - 1] = ch[i + t8 - 1] + ch[i + t9 - 1];
				cc[ic + t6 - 1] = ch[i + t8 - 1] - ch[i + t9 - 1];
				cc[i + t7] = ch[i + t8] + ch[i + t9];
				cc[ic + t6] = ch[i + t9] - ch[i + t8];
			}
			t6 += t10;
			t7 += t10;
			t8 += ido;
			t9 += ido;
		}
	}
	return;

L141:

	t1 = -ido;
	t3 = 0;
	t4 = 0;
	t5 = ipp2*t0;
	for (j = 1; j<ipph; j++){
		t1 += t2;
		t3 += t2;
		t4 += t0;
		t5 -= t0;
		for (i = 2; i<ido; i += 2){
			t6 = idp2 + t1 - i;
			t7 = i + t3;
			t8 = i + t4;
			t9 = i + t5;
			for (k = 0; k<l1; k++){
				cc[t7 - 1] = ch[t8 - 1] + ch[t9 - 1];
				cc[t6 - 1] = ch[t8 - 1] - ch[t9 - 1];
				cc[t7] = ch[t8] + ch[t9];
				cc[t6] = ch[t9] - ch[t8];
				t6 += t10;
				t7 += t10;
				t8 += ido;
				t9 += ido;
			}
		}
	}
}

STIN void drftf1(int n, float *c, float *ch, float *wa, int *ifac){
	int i, k1, l1, l2;
	int na, kh, nf;
	int ip, iw, ido, idl1, ix2, ix3;

	nf = ifac[1];
	na = 1;
	l2 = n;
	iw = n;

	for (k1 = 0; k1<nf; k1++){
		kh = nf - k1;
		ip = ifac[kh + 1];
		l1 = l2 / ip;
		ido = n / l2;
		idl1 = ido*l1;
		iw -= (ip - 1)*ido;
		na = 1 - na;

		if (ip != 4)goto L102;

		ix2 = iw + ido;
		ix3 = ix2 + ido;
		if (na != 0)
			dradf4(ido, l1, ch, c, wa + iw - 1, wa + ix2 - 1, wa + ix3 - 1);
		else
			dradf4(ido, l1, c, ch, wa + iw - 1, wa + ix2 - 1, wa + ix3 - 1);
		goto L110;

	L102:
		if (ip != 2)goto L104;
		if (na != 0)goto L103;

		dradf2(ido, l1, c, ch, wa + iw - 1);
		goto L110;

	L103:
		dradf2(ido, l1, ch, c, wa + iw - 1);
		goto L110;

	L104:
		if (ido == 1)na = 1 - na;
		if (na != 0)goto L109;

		dradfg(ido, ip, l1, idl1, c, c, c, ch, ch, wa + iw - 1);
		na = 1;
		goto L110;

	L109:
		dradfg(ido, ip, l1, idl1, ch, ch, ch, c, c, wa + iw - 1);
		na = 0;

	L110:
		l2 = l1;
	}

	if (na == 1)return;

	for (i = 0; i<n; i++)c[i] = ch[i];
}

void __ogg_fdrfftf(int n, float *r, float *wsave, int *ifac){
	if (n == 1)return;
	drftf1(n, r, wsave, wsave + n, ifac);
}

STIN void dcsqf1(int n, float *x, float *w, float *xh, int *ifac){
	int modn, i, k, kc;
	int np2, ns2;
	float xim1;

	ns2 = (n + 1) >> 1;
	np2 = n;

	kc = np2;
	for (k = 1; k<ns2; k++){
		kc--;
		xh[k] = x[k] + x[kc];
		xh[kc] = x[k] - x[kc];
	}

	modn = n % 2;
	if (modn == 0)xh[ns2] = x[ns2] + x[ns2];

	for (k = 1; k<ns2; k++){
		kc = np2 - k;
		x[k] = w[k - 1] * xh[kc] + w[kc - 1] * xh[k];
		x[kc] = w[k - 1] * xh[k] - w[kc - 1] * xh[kc];
	}

	if (modn == 0)x[ns2] = w[ns2 - 1] * xh[ns2];

	__ogg_fdrfftf(n, x, xh, ifac);

	for (i = 2; i<n; i += 2){
		xim1 = x[i - 1] - x[i];
		x[i] = x[i - 1] + x[i];
		x[i - 1] = xim1;
	}
}

void __ogg_fdcosqf(int n, float *x, float *wsave, int *ifac){
	static float sqrt2 = 1.4142135623730950488016887242097;
	float tsqx;

	switch (n){
	case 0:case 1:
		return;
	case 2:
		tsqx = sqrt2*x[1];
		x[1] = x[0] - tsqx;
		x[0] += tsqx;
		return;
	default:
		dcsqf1(n, x, wsave, wsave + n, ifac);
		return;
	}
}

STIN void dradb2(int ido, int l1, float *cc, float *ch, float *wa1){
	int i, k, t0, t1, t2, t3, t4, t5, t6;
	float ti2, tr2;

	t0 = l1*ido;

	t1 = 0;
	t2 = 0;
	t3 = (ido << 1) - 1;
	for (k = 0; k<l1; k++){
		ch[t1] = cc[t2] + cc[t3 + t2];
		ch[t1 + t0] = cc[t2] - cc[t3 + t2];
		t2 = (t1 += ido) << 1;
	}

	if (ido<2)return;
	if (ido == 2)goto L105;

	t1 = 0;
	t2 = 0;
	for (k = 0; k<l1; k++){
		t3 = t1;
		t5 = (t4 = t2) + (ido << 1);
		t6 = t0 + t1;
		for (i = 2; i<ido; i += 2){
			t3 += 2;
			t4 += 2;
			t5 -= 2;
			t6 += 2;
			ch[t3 - 1] = cc[t4 - 1] + cc[t5 - 1];
			tr2 = cc[t4 - 1] - cc[t5 - 1];
			ch[t3] = cc[t4] - cc[t5];
			ti2 = cc[t4] + cc[t5];
			ch[t6 - 1] = wa1[i - 2] * tr2 - wa1[i - 1] * ti2;
			ch[t6] = wa1[i - 2] * ti2 + wa1[i - 1] * tr2;
		}
		t2 = (t1 += ido) << 1;
	}

	if (ido % 2 == 1)return;

L105:
	t1 = ido - 1;
	t2 = ido - 1;
	for (k = 0; k<l1; k++){
		ch[t1] = cc[t2] + cc[t2];
		ch[t1 + t0] = -(cc[t2 + 1] + cc[t2 + 1]);
		t1 += ido;
		t2 += ido << 1;
	}
}

STIN void dradb3(int ido, int l1, float *cc, float *ch, float *wa1,
	float *wa2){
	static float taur = -.5;
	static float taui = .86602540378443864676372317075293618;
	int i, k, t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
	float ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
	t0 = l1*ido;

	t1 = 0;
	t2 = t0 << 1;
	t3 = ido << 1;
	t4 = ido + (ido << 1);
	t5 = 0;
	for (k = 0; k<l1; k++){
		tr2 = cc[t3 - 1] + cc[t3 - 1];
		cr2 = cc[t5] + (taur*tr2);
		ch[t1] = cc[t5] + tr2;
		ci3 = taui*(cc[t3] + cc[t3]);
		ch[t1 + t0] = cr2 - ci3;
		ch[t1 + t2] = cr2 + ci3;
		t1 += ido;
		t3 += t4;
		t5 += t4;
	}

	if (ido == 1)return;

	t1 = 0;
	t3 = ido << 1;
	for (k = 0; k<l1; k++){
		t7 = t1 + (t1 << 1);
		t6 = (t5 = t7 + t3);
		t8 = t1;
		t10 = (t9 = t1 + t0) + t0;

		for (i = 2; i<ido; i += 2){
			t5 += 2;
			t6 -= 2;
			t7 += 2;
			t8 += 2;
			t9 += 2;
			t10 += 2;
			tr2 = cc[t5 - 1] + cc[t6 - 1];
			cr2 = cc[t7 - 1] + (taur*tr2);
			ch[t8 - 1] = cc[t7 - 1] + tr2;
			ti2 = cc[t5] - cc[t6];
			ci2 = cc[t7] + (taur*ti2);
			ch[t8] = cc[t7] + ti2;
			cr3 = taui*(cc[t5 - 1] - cc[t6 - 1]);
			ci3 = taui*(cc[t5] + cc[t6]);
			dr2 = cr2 - ci3;
			dr3 = cr2 + ci3;
			di2 = ci2 + cr3;
			di3 = ci2 - cr3;
			ch[t9 - 1] = wa1[i - 2] * dr2 - wa1[i - 1] * di2;
			ch[t9] = wa1[i - 2] * di2 + wa1[i - 1] * dr2;
			ch[t10 - 1] = wa2[i - 2] * dr3 - wa2[i - 1] * di3;
			ch[t10] = wa2[i - 2] * di3 + wa2[i - 1] * dr3;
		}
		t1 += ido;
	}
}

STIN void dradb4(int ido, int l1, float *cc, float *ch, float *wa1,
	float *wa2, float *wa3){
	static float sqrt2 = 1.4142135623730950488016887242097;
	int i, k, t0, t1, t2, t3, t4, t5, t6, t7, t8;
	float ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
	t0 = l1*ido;

	t1 = 0;
	t2 = ido << 2;
	t3 = 0;
	t6 = ido << 1;
	for (k = 0; k<l1; k++){
		t4 = t3 + t6;
		t5 = t1;
		tr3 = cc[t4 - 1] + cc[t4 - 1];
		tr4 = cc[t4] + cc[t4];
		tr1 = cc[t3] - cc[(t4 += t6) - 1];
		tr2 = cc[t3] + cc[t4 - 1];
		ch[t5] = tr2 + tr3;
		ch[t5 += t0] = tr1 - tr4;
		ch[t5 += t0] = tr2 - tr3;
		ch[t5 += t0] = tr1 + tr4;
		t1 += ido;
		t3 += t2;
	}

	if (ido<2)return;
	if (ido == 2)goto L105;

	t1 = 0;
	for (k = 0; k<l1; k++){
		t5 = (t4 = (t3 = (t2 = t1 << 2) + t6)) + t6;
		t7 = t1;
		for (i = 2; i<ido; i += 2){
			t2 += 2;
			t3 += 2;
			t4 -= 2;
			t5 -= 2;
			t7 += 2;
			ti1 = cc[t2] + cc[t5];
			ti2 = cc[t2] - cc[t5];
			ti3 = cc[t3] - cc[t4];
			tr4 = cc[t3] + cc[t4];
			tr1 = cc[t2 - 1] - cc[t5 - 1];
			tr2 = cc[t2 - 1] + cc[t5 - 1];
			ti4 = cc[t3 - 1] - cc[t4 - 1];
			tr3 = cc[t3 - 1] + cc[t4 - 1];
			ch[t7 - 1] = tr2 + tr3;
			cr3 = tr2 - tr3;
			ch[t7] = ti2 + ti3;
			ci3 = ti2 - ti3;
			cr2 = tr1 - tr4;
			cr4 = tr1 + tr4;
			ci2 = ti1 + ti4;
			ci4 = ti1 - ti4;

			ch[(t8 = t7 + t0) - 1] = wa1[i - 2] * cr2 - wa1[i - 1] * ci2;
			ch[t8] = wa1[i - 2] * ci2 + wa1[i - 1] * cr2;
			ch[(t8 += t0) - 1] = wa2[i - 2] * cr3 - wa2[i - 1] * ci3;
			ch[t8] = wa2[i - 2] * ci3 + wa2[i - 1] * cr3;
			ch[(t8 += t0) - 1] = wa3[i - 2] * cr4 - wa3[i - 1] * ci4;
			ch[t8] = wa3[i - 2] * ci4 + wa3[i - 1] * cr4;
		}
		t1 += ido;
	}

	if (ido % 2 == 1)return;

L105:

	t1 = ido;
	t2 = ido << 2;
	t3 = ido - 1;
	t4 = ido + (ido << 1);
	for (k = 0; k<l1; k++){
		t5 = t3;
		ti1 = cc[t1] + cc[t4];
		ti2 = cc[t4] - cc[t1];
		tr1 = cc[t1 - 1] - cc[t4 - 1];
		tr2 = cc[t1 - 1] + cc[t4 - 1];
		ch[t5] = tr2 + tr2;
		ch[t5 += t0] = sqrt2*(tr1 - ti1);
		ch[t5 += t0] = ti2 + ti2;
		ch[t5 += t0] = -sqrt2*(tr1 + ti1);

		t3 += ido;
		t1 += t2;
		t4 += t2;
	}
}

STIN void dradbg(int ido, int ip, int l1, int idl1, float *cc, float *c1,
	float *c2, float *ch, float *ch2, float *wa){
	static float tpi = 6.28318530717958647692528676655900577;
	int idij, ipph, i, j, k, l, ik, is, t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10,
		t11, t12;
	float dc2, ai1, ai2, ar1, ar2, ds2;
	int nbd;
	float dcp, arg, dsp, ar1h, ar2h;
	int ipp2;

	t10 = ip*ido;
	t0 = l1*ido;
	arg = tpi / (float)ip;
	dcp = cos(arg);
	dsp = sin(arg);
	nbd = (ido - 1) >> 1;
	ipp2 = ip;
	ipph = (ip + 1) >> 1;
	if (ido<l1)goto L103;

	t1 = 0;
	t2 = 0;
	for (k = 0; k<l1; k++){
		t3 = t1;
		t4 = t2;
		for (i = 0; i<ido; i++){
			ch[t3] = cc[t4];
			t3++;
			t4++;
		}
		t1 += ido;
		t2 += t10;
	}
	goto L106;

L103:
	t1 = 0;
	for (i = 0; i<ido; i++){
		t2 = t1;
		t3 = t1;
		for (k = 0; k<l1; k++){
			ch[t2] = cc[t3];
			t2 += ido;
			t3 += t10;
		}
		t1++;
	}

L106:
	t1 = 0;
	t2 = ipp2*t0;
	t7 = (t5 = ido << 1);
	for (j = 1; j<ipph; j++){
		t1 += t0;
		t2 -= t0;
		t3 = t1;
		t4 = t2;
		t6 = t5;
		for (k = 0; k<l1; k++){
			ch[t3] = cc[t6 - 1] + cc[t6 - 1];
			ch[t4] = cc[t6] + cc[t6];
			t3 += ido;
			t4 += ido;
			t6 += t10;
		}
		t5 += t7;
	}

	if (ido == 1)goto L116;
	if (nbd<l1)goto L112;

	t1 = 0;
	t2 = ipp2*t0;
	t7 = 0;
	for (j = 1; j<ipph; j++){
		t1 += t0;
		t2 -= t0;
		t3 = t1;
		t4 = t2;

		t7 += (ido << 1);
		t8 = t7;
		for (k = 0; k<l1; k++){
			t5 = t3;
			t6 = t4;
			t9 = t8;
			t11 = t8;
			for (i = 2; i<ido; i += 2){
				t5 += 2;
				t6 += 2;
				t9 += 2;
				t11 -= 2;
				ch[t5 - 1] = cc[t9 - 1] + cc[t11 - 1];
				ch[t6 - 1] = cc[t9 - 1] - cc[t11 - 1];
				ch[t5] = cc[t9] - cc[t11];
				ch[t6] = cc[t9] + cc[t11];
			}
			t3 += ido;
			t4 += ido;
			t8 += t10;
		}
	}
	goto L116;

L112:
	t1 = 0;
	t2 = ipp2*t0;
	t7 = 0;
	for (j = 1; j<ipph; j++){
		t1 += t0;
		t2 -= t0;
		t3 = t1;
		t4 = t2;
		t7 += (ido << 1);
		t8 = t7;
		t9 = t7;
		for (i = 2; i<ido; i += 2){
			t3 += 2;
			t4 += 2;
			t8 += 2;
			t9 -= 2;
			t5 = t3;
			t6 = t4;
			t11 = t8;
			t12 = t9;
			for (k = 0; k<l1; k++){
				ch[t5 - 1] = cc[t11 - 1] + cc[t12 - 1];
				ch[t6 - 1] = cc[t11 - 1] - cc[t12 - 1];
				ch[t5] = cc[t11] - cc[t12];
				ch[t6] = cc[t11] + cc[t12];
				t5 += ido;
				t6 += ido;
				t11 += t10;
				t12 += t10;
			}
		}
	}

L116:
	ar1 = 1.;
	ai1 = 0.;
	t1 = 0;
	t9 = (t2 = ipp2*idl1);
	t3 = (ip - 1)*idl1;
	for (l = 1; l<ipph; l++){
		t1 += idl1;
		t2 -= idl1;

		ar1h = dcp*ar1 - dsp*ai1;
		ai1 = dcp*ai1 + dsp*ar1;
		ar1 = ar1h;
		t4 = t1;
		t5 = t2;
		t6 = 0;
		t7 = idl1;
		t8 = t3;
		for (ik = 0; ik<idl1; ik++){
			c2[t4++] = ch2[t6++] + ar1*ch2[t7++];
			c2[t5++] = ai1*ch2[t8++];
		}
		dc2 = ar1;
		ds2 = ai1;
		ar2 = ar1;
		ai2 = ai1;

		t6 = idl1;
		t7 = t9 - idl1;
		for (j = 2; j<ipph; j++){
			t6 += idl1;
			t7 -= idl1;
			ar2h = dc2*ar2 - ds2*ai2;
			ai2 = dc2*ai2 + ds2*ar2;
			ar2 = ar2h;
			t4 = t1;
			t5 = t2;
			t11 = t6;
			t12 = t7;
			for (ik = 0; ik<idl1; ik++){
				c2[t4++] += ar2*ch2[t11++];
				c2[t5++] += ai2*ch2[t12++];
			}
		}
	}

	t1 = 0;
	for (j = 1; j<ipph; j++){
		t1 += idl1;
		t2 = t1;
		for (ik = 0; ik<idl1; ik++)ch2[ik] += ch2[t2++];
	}

	t1 = 0;
	t2 = ipp2*t0;
	for (j = 1; j<ipph; j++){
		t1 += t0;
		t2 -= t0;
		t3 = t1;
		t4 = t2;
		for (k = 0; k<l1; k++){
			ch[t3] = c1[t3] - c1[t4];
			ch[t4] = c1[t3] + c1[t4];
			t3 += ido;
			t4 += ido;
		}
	}

	if (ido == 1)goto L132;
	if (nbd<l1)goto L128;

	t1 = 0;
	t2 = ipp2*t0;
	for (j = 1; j<ipph; j++){
		t1 += t0;
		t2 -= t0;
		t3 = t1;
		t4 = t2;
		for (k = 0; k<l1; k++){
			t5 = t3;
			t6 = t4;
			for (i = 2; i<ido; i += 2){
				t5 += 2;
				t6 += 2;
				ch[t5 - 1] = c1[t5 - 1] - c1[t6];
				ch[t6 - 1] = c1[t5 - 1] + c1[t6];
				ch[t5] = c1[t5] + c1[t6 - 1];
				ch[t6] = c1[t5] - c1[t6 - 1];
			}
			t3 += ido;
			t4 += ido;
		}
	}
	goto L132;

L128:
	t1 = 0;
	t2 = ipp2*t0;
	for (j = 1; j<ipph; j++){
		t1 += t0;
		t2 -= t0;
		t3 = t1;
		t4 = t2;
		for (i = 2; i<ido; i += 2){
			t3 += 2;
			t4 += 2;
			t5 = t3;
			t6 = t4;
			for (k = 0; k<l1; k++){
				ch[t5 - 1] = c1[t5 - 1] - c1[t6];
				ch[t6 - 1] = c1[t5 - 1] + c1[t6];
				ch[t5] = c1[t5] + c1[t6 - 1];
				ch[t6] = c1[t5] - c1[t6 - 1];
				t5 += ido;
				t6 += ido;
			}
		}
	}

L132:
	if (ido == 1)return;

	for (ik = 0; ik<idl1; ik++)c2[ik] = ch2[ik];

	t1 = 0;
	for (j = 1; j<ip; j++){
		t2 = (t1 += t0);
		for (k = 0; k<l1; k++){
			c1[t2] = ch[t2];
			t2 += ido;
		}
	}

	if (nbd>l1)goto L139;

	is = -ido - 1;
	t1 = 0;
	for (j = 1; j<ip; j++){
		is += ido;
		t1 += t0;
		idij = is;
		t2 = t1;
		for (i = 2; i<ido; i += 2){
			t2 += 2;
			idij += 2;
			t3 = t2;
			for (k = 0; k<l1; k++){
				c1[t3 - 1] = wa[idij - 1] * ch[t3 - 1] - wa[idij] * ch[t3];
				c1[t3] = wa[idij - 1] * ch[t3] + wa[idij] * ch[t3 - 1];
				t3 += ido;
			}
		}
	}
	return;

L139:
	is = -ido - 1;
	t1 = 0;
	for (j = 1; j<ip; j++){
		is += ido;
		t1 += t0;
		t2 = t1;
		for (k = 0; k<l1; k++){
			idij = is;
			t3 = t2;
			for (i = 2; i<ido; i += 2){
				idij += 2;
				t3 += 2;
				c1[t3 - 1] = wa[idij - 1] * ch[t3 - 1] - wa[idij] * ch[t3];
				c1[t3] = wa[idij - 1] * ch[t3] + wa[idij] * ch[t3 - 1];
			}
			t2 += ido;
		}
	}
}

STIN void drftb1(int n, float *c, float *ch, float *wa, int *ifac){
	int i, k1, l1, l2;
	int na;
	int nf, ip, iw, ix2, ix3, ido, idl1;

	nf = ifac[1];
	na = 0;
	l1 = 1;
	iw = 1;

	for (k1 = 0; k1<nf; k1++){
		ip = ifac[k1 + 2];
		l2 = ip*l1;
		ido = n / l2;
		idl1 = ido*l1;
		if (ip != 4)goto L103;
		ix2 = iw + ido;
		ix3 = ix2 + ido;

		if (na != 0)
			dradb4(ido, l1, ch, c, wa + iw - 1, wa + ix2 - 1, wa + ix3 - 1);
		else
			dradb4(ido, l1, c, ch, wa + iw - 1, wa + ix2 - 1, wa + ix3 - 1);
		na = 1 - na;
		goto L115;

	L103:
		if (ip != 2)goto L106;

		if (na != 0)
			dradb2(ido, l1, ch, c, wa + iw - 1);
		else
			dradb2(ido, l1, c, ch, wa + iw - 1);
		na = 1 - na;
		goto L115;

	L106:
		if (ip != 3)goto L109;

		ix2 = iw + ido;
		if (na != 0)
			dradb3(ido, l1, ch, c, wa + iw - 1, wa + ix2 - 1);
		else
			dradb3(ido, l1, c, ch, wa + iw - 1, wa + ix2 - 1);
		na = 1 - na;
		goto L115;

	L109:
		/*    The radix five case can be translated later..... */
		/*    if(ip!=5)goto L112;

		ix2=iw+ido;
		ix3=ix2+ido;
		ix4=ix3+ido;
		if(na!=0)
		dradb5(ido,l1,ch,c,wa+iw-1,wa+ix2-1,wa+ix3-1,wa+ix4-1);
		else
		dradb5(ido,l1,c,ch,wa+iw-1,wa+ix2-1,wa+ix3-1,wa+ix4-1);
		na=1-na;
		goto L115;

		L112:*/
		if (na != 0)
			dradbg(ido, ip, l1, idl1, ch, ch, ch, c, c, wa + iw - 1);
		else
			dradbg(ido, ip, l1, idl1, c, c, c, ch, ch, wa + iw - 1);
		if (ido == 1)na = 1 - na;

	L115:
		l1 = l2;
		iw += (ip - 1)*ido;
	}

	if (na == 0)return;

	for (i = 0; i<n; i++)c[i] = ch[i];
}

void __ogg_fdrfftb(int n, float *r, float *wsave, int *ifac){
	if (n == 1)return;
	drftb1(n, r, wsave, wsave + n, ifac);
}

STIN void dcsqb1(int n, float *x, float *w, float *xh, int *ifac){
	int modn, i, k, kc;
	int np2, ns2;
	float xim1;

	ns2 = (n + 1) >> 1;
	np2 = n;

	for (i = 2; i<n; i += 2){
		xim1 = x[i - 1] + x[i];
		x[i] -= x[i - 1];
		x[i - 1] = xim1;
	}

	x[0] += x[0];
	modn = n % 2;
	if (modn == 0)x[n - 1] += x[n - 1];

	__ogg_fdrfftb(n, x, xh, ifac);

	kc = np2;
	for (k = 1; k<ns2; k++){
		kc--;
		xh[k] = w[k - 1] * x[kc] + w[kc - 1] * x[k];
		xh[kc] = w[k - 1] * x[k] - w[kc - 1] * x[kc];
	}

	if (modn == 0)x[ns2] = w[ns2 - 1] * (x[ns2] + x[ns2]);

	kc = np2;
	for (k = 1; k<ns2; k++){
		kc--;
		x[k] = xh[k] + xh[kc];
		x[kc] = xh[k] - xh[kc];
	}
	x[0] += x[0];
}

void __ogg_fdcosqb(int n, float *x, float *wsave, int *ifac){
	static float tsqrt2 = 2.8284271247461900976033774484194;
	float x1;

	if (n<2){
		x[0] *= 4;
		return;
	}
	if (n == 2){
		x1 = (x[0] + x[1]) * 4;
		x[1] = tsqrt2*(x[0] - x[1]);
		x[0] = x1;
		return;
	}

	dcsqb1(n, x, wsave, wsave + n, ifac);
}


